According the ever-loving wiki on mirrors
For technical applications such as laser mirrors, ... [] ... and achieve reflectivities of 90–95% when new. ... [] ... Applications requiring higher reflectivity or greater durability where wide bandwidth is not essential use dielectric coatings, which can achieve reflectivities as high as 99.999% over a narrow range of wavelengths.
So we need a laser, some dielectric coatings (whatever that means), and a perfect sealed sphere…
Then we’re making the first Fluther science fair project in your back yard. Go team.